Rupp hit St. Louis forward T.J. Oshie high midway through the second period of the Wild's victory on Thursday night.
Rupp was playing for the first time in 24 games for Minnesota.
Blues coach Ken Hitchcock said after the game that Oshie was day-to-day with his head injury.
The club called up Ty Rattie on Friday for their game against Dallas.
Rupp, 34, will be suspended for Minnesota's final regula- season game this weekend, plus their first three playoff games.
He will also forfeit just under $7,700 US in salary.
It is the first official ruling with Stephane Quintal at the helm of the NHL Department of Player Safety. Quintal has assumed the role through the playoffs as predecessor Brendan Shanahan has been hired as president of the Toronto Maple Leafs.
Here's the NHL's explanation for the decision: